SinX/secX = 1/(tanX+cotX)

Verifying trig. identities for Honors Pre Calc

sin x/sec x = sin x / (1/cos x) = sin x cos x

1/(tan x + cot x) = 1/(sin x/cos x + cos x/sin x)
= 1/((sin^2 x + cos^2 x)/(sin x cos x)
= sin x cos x / (sin^2 x + cos^2 x) = sin x cos x

sin x cos x = sin x cos x

sinx/secx=1/(tanx+cotx)
cosx/sinx+sinx/cosx
2cosxsinx/sinxcosx
cosxsinx=sinx/1(cosx/1)
cosxsinx=cosxsinx

That one is weird. There's probably a way to make either the RHS or LHS equal to the other, but I found making each of them equal to each other easier.